Subnetting example 4

If I add up 128+64+32+16+8+4+2+1 we get 255

When we borrow a digit from the network we double 256 (256+256) then -(2) Subtract 1 for the subnet IP and 1 for the Broadcast IP

```
1. 192.168.00000000 |.00000000 /24 (254 hosts) 256-(2)=254 (2) being the Subnet IP and the Broadcast IP
2. 192.168.0000000 | 0.00000000 /23 (510 hosts) If we borrow 1 bit from the network side we can double our host. 256+256=512-(2)=510
3. 192.168.000000 | 00.00000000 /22 (1022 hosts) If we borrow another 1 bit from the network side we can double our host again. answer 512+512=1024-(2)=1022
4. 192.168.00000 | 000.00000000 /21 (2046 hosts) If we borrow another 1 bit from the network side we can double our host again. 1024+1024=2048-(2)=2046
```

**If I add up 128+64+32+16+8+4+2+1 we get 255**

**Why do we double 256 and not 255**

This has to do with the limitations of representing 8 bit binary numbers. A doubling of 255, in our decimal thinking is that place values do not change, for example, if we add 1+ 255 = 256. This is the way you're thinking. But it changes if we add 1 + 999 = 1000. Notice that we've added **a place value**, not a value between. The same would be true if we do 9999 + 1 = 10000. this change is that each place holder you add changes by 10.

The same is true here in binary, the 8 bits you're referring to in networking are the HOST bits ( all the numbers are part of the group). The NETWORK ID are the place value numbers--the Group Number that represents all the HOST bits). The different is that you're not talking about powers of 10 for place holder change but by 2 (or doubling). What you're seeing at the end with 255 is really equivalent to 99, 999, 9999... and rolling over to the next place value.

]]>